1,424 research outputs found
A quantum Jensen-Shannon graph kernel for unattributed graphs
In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel
Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence
In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection
HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification
In this work, we propose a family of novel quantum kernels, namely the
Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed
graphs. Different from most existing classical graph kernels, the proposed
HAQJSK kernels can incorporate hierarchical aligned structure information
between graphs and transform graphs of random sizes into fixed-sized aligned
graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of
vertices and the Hierarchical Transitive Aligned Density Matrix of the
Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the
resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon
Divergence (QJSD) between their transitive aligned graph structures. We show
that the proposed HAQJSK kernels not only reflect richer intrinsic global graph
characteristics in terms of the CTQW, but also address the drawback of
neglecting structural correspondence information arising in most existing
R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon
Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can
simultaneously guarantee the properties of permutation invariant and positive
definiteness, explaining the theoretical advantages of the HAQJSK kernels.
Experiments indicate the effectiveness of the proposed kernels
Graph Convolutional Neural Networks based on Quantum Vertex Saliency
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network
(QSGCNN) model that can directly learn a classification function for graphs of
arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network
(GCNN) models, the proposed QSGCNN model incorporates the process of
identifying transitive aligned vertices between graphs, and transforms
arbitrary sized graphs into fixed-sized aligned vertex grid structures. In
order to learn representative graph characteristics, a new quantum spatial
graph convolution is proposed and employed to extract multi-scale vertex
features, in terms of quantum information propagation between grid vertices of
each graph. Since the quantum spatial convolution preserves the grid structures
of the input vertices (i.e., the convolution layer does not change the original
spatial sequence of vertices), the proposed QSGCNN model allows to directly
employ the traditional convolutional neural network architecture to further
learn from the global graph topology, providing an end-to-end deep learning
architecture that integrates the graph representation and learning in the
quantum spatial graph convolution layer and the traditional convolutional layer
for graph classifications. We demonstrate the effectiveness of the proposed
QSGCNN model in relation to existing state-of-the-art methods. The proposed
QSGCNN model addresses the shortcomings of information loss and imprecise
information representation arising in existing GCN models associated with the
use of SortPooling or SumPooling layers. Experiments on benchmark graph
classification datasets demonstrate the effectiveness of the proposed QSGCNN
model
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